AP EAPCET 2024 - 21th May Morning Shift | Matrices and Determinants Question 1 | Mathematics

If $A=\left|\begin{array}{lll}2 & 3 & 4 \\ 1 & k & 2 \\ 4 & 1 & 5\end{array}\right|$ is singular matrix, then the quadratic equation having the roots $k$ an $\frac{1}{k}$ is

$6 x^2+13 x+6=0$

$12 x^2-25 x+12=0$

$6 x^2-13 x+6=0$

$2 x^2-5 x+2=0$

AP EAPCET 2024 - 21th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $A$ be a $4 \times 4$ matrix and $P$ be is adjoint matrix, If $|P|=\left|\frac{A}{2}\right|$ then $\left|A^{-1}\right|$

$\pm \frac{1}{4}$

$\pm 8$

$\pm 2$

$\pm 4$

AP EAPCET 2024 - 21th May Morning Shift

MCQ (Single Correct Answer)

-0

The system $x+2 y+3 z=4,4 x+5 y+3 z=5,3 x+4 y+3 z=\lambda$ is consistent and $3 \lambda=n+100$, then $n=$

-42

-86

-24

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

$\left|\begin{array}{ccc}a & b & c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1\end{array}\right|$ is not equal to

$\left|\begin{array}{ccc}a+1 & b+1 & c+1 \\ a^2+1 & b^2+1 & c^2+1 \\ 1 & 1 & 1\end{array}\right|$

$\left|\begin{array}{ccc}a-b & b-c & c \\ a^2-b^2 & b^2-c^2 & c^2 \\ 0 & 0 & 1\end{array}\right|$

$\left|\begin{array}{ccc}a(a+1) & b(b+1) & c(c+1) \\ a+1 & b+1 & c+1 \\ -1 & -1 & -1\end{array}\right|$

$\left|\begin{array}{ccc}a+b & b+c & c+a \\ a^2+b^2 & b^2+c^2 & c^2+a^2 \\ 2 & 2 & 2\end{array}\right|$

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